August 2023 A cross-validation framework for signal denoising with applications to trend filtering, dyadic CART and beyond
Anamitra Chaudhuri, Sabyasachi Chatterjee
Author Affiliations +
Ann. Statist. 51(4): 1534-1560 (August 2023). DOI: 10.1214/23-AOS2283

Abstract

This paper formulates a general cross-validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as trend filtering and dyadic CART. The resulting cross-validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross-validated versions of trend filtering or dyadic CART. To illustrate the generality of the framework, we also propose and study cross-validated versions of two fundamental estimators; lasso for high-dimensional linear regression and singular value thresholding for matrix estimation. Our general framework is inspired by the ideas in Chatterjee and Jafarov (2015) and is potentially applicable to a wide range of estimation methods which use tuning parameters.

Funding Statement

The second author is supported by NSF Grant DMS-1916375.

Citation

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Anamitra Chaudhuri. Sabyasachi Chatterjee. "A cross-validation framework for signal denoising with applications to trend filtering, dyadic CART and beyond." Ann. Statist. 51 (4) 1534 - 1560, August 2023. https://doi.org/10.1214/23-AOS2283

Information

Received: 1 January 2022; Revised: 1 March 2023; Published: August 2023
First available in Project Euclid: 19 October 2023

Digital Object Identifier: 10.1214/23-AOS2283

Subjects:
Primary: 62G05 , 62G08

Keywords: adaptive risk bounds , cross-validation , Dyadic CART , Lasso , singular value thresholding , Trend filtering

Rights: Copyright © 2023 Institute of Mathematical Statistics

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Vol.51 • No. 4 • August 2023
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